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Analytic Theory of Itô-Stochastic Differential Equations with Non-smooth Coefficients (SpringerBriefs in Probability and Mathematical Statistics) - Softcover
- PublisherSpringer
- Publication date2022
- ISBN 10 981193830X
- ISBN 13 9789811938306
- BindingPaperback
- LanguageEnglish
- Edition number1
- Number of pages144
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Analytic Theory of It�-Stochastic Differential Equations with Non-smooth Coefficients
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Analytic Theory of Itô-Stochastic Differential Equations with Non-smooth Coefficients (SpringerBriefs in Probability and Mathematical Statistics)
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Analytic Theory of Itô-Stochastic Differential Equations with Non-smooth Coefficients (SpringerBriefs in Probability and Mathematical Statistics)
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Analytic Theory of Itô-Stochastic Differential Equations with Non-smooth Coefficients (SpringerBriefs in Probability and Mathematical Statistics)
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Analytic Theory of Itô-Stochastic Differential Equations with Non-smooth Coefficients
Published by
Springer Nature Singapore, Springer Nature Singapore Aug 2022, 2022
ISBN 10: 981193830X
ISBN 13: 9789811938306
New
Taschenbuch
Seller: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Germany
Seller rating 5 out of 5 stars
Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This book provides analytic tools to describe local and global behavior of solutions to Itô-stochastic differential equations with non-degenerate Sobolev diffusion coefficients and locally integrable drift.Regularity theory of partial differential equations is applied to construct such solutions and to obtain strong Feller properties, irreducibility, Krylov-type estimates, moment inequalities, various types of non-explosion criteria, and long time behavior, e.g., transience, recurrence, and convergence to stationarity.The approach is based on the realization of the transition semigroup associated with the solution of a stochastic differential equation as a strongly continuous semigroup in theLp-space with respect to a weight that plays the role of a sub-stationary or stationary density. This way we obtain in particular a rigorous functional analytic description of the generator of the solution of a stochastic differential equation and its full domain. The existence of such a weight is shown under broad assumptions on the coefficients. A remarkable fact is that although the weight may not be unique, many important results are independent of it.Given such a weight and semigroup, one can construct and further analyze in detail a weak solution to the stochastic differential equation combining variational techniques, regularity theory for partial differential equations, potential, and generalized Dirichlet form theory.Under classical-like or various other criteria for non-explosion we obtain as one of our main applications the existence of a pathwise unique and strong solution with an infinite lifetime. These results substantially supplement the classical case of locally Lipschitz or monotone coefficients.We further treat other types of uniqueness and non-uniqueness questions, such as uniqueness and non-uniqueness of the mentioned weights and uniqueness in law, in a certain sense, of the solution. 144 pp. Englisch. Seller Inventory # 9789811938306
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Analytic Theory of Itô-Stochastic Differential Equations with Non-smooth Coefficients
Published by
Springer Nature Singapore, Springer Nature Singapore, 2022
ISBN 10: 981193830X
ISBN 13: 9789811938306
New
Taschenbuch
Seller: AHA-BUCH GmbH, Einbeck, Germany
Seller rating 5 out of 5 stars
Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - This book provides analytic tools to describe local and global behavior of solutions to Itô-stochastic differential equations with non-degenerate Sobolev diffusion coefficients and locally integrable drift.Regularity theory of partial differential equations is applied to construct such solutions and to obtain strong Feller properties, irreducibility, Krylov-type estimates, moment inequalities, various types of non-explosion criteria, and long time behavior, e.g., transience, recurrence, and convergence to stationarity.The approach is based on the realization of the transition semigroup associated with the solution of a stochastic differential equation as a strongly continuous semigroup in theLp-space with respect to a weight that plays the role of a sub-stationary or stationary density. This way we obtain in particular a rigorous functional analytic description of the generator of the solution of a stochastic differential equation and its full domain. The existence of such a weight is shown under broad assumptions on the coefficients. A remarkable fact is that although the weight may not be unique, many important results are independent of it.Given such a weight and semigroup, one can construct and further analyze in detail a weak solution to the stochastic differential equation combining variational techniques, regularity theory for partial differential equations, potential, and generalized Dirichlet form theory.Under classical-like or various other criteria for non-explosion we obtain as one of our main applications the existence of a pathwise unique and strong solution with an infinite lifetime. These results substantially supplement the classical case of locally Lipschitz or monotone coefficients.We further treat other types of uniqueness and non-uniqueness questions, such as uniqueness and non-uniqueness of the mentioned weights and uniqueness in law, in a certain sense, of the solution. Seller Inventory # 9789811938306
Quantity: 1 available
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Analytic Theory of Itô-Stochastic Differential Equations with Non-smooth Coefficients
Published by
Springer Nature Singapore, 2022
ISBN 10: 981193830X
ISBN 13: 9789811938306
New
Softcover
Seller: moluna, Greven, Germany
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Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Presents local and global properties of stochastic differential equations under minimal assumptions (state of the art) Shows the missing link between regularity theory of partial differential equations and stochastic differential equationsP. Seller Inventory # 600122667
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